Finite Group Databasebeta

← C2×#11736391 #14217866

Subgroups — C2×#11736391 #14217866

Order 1792.

2810 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic7C211yesmaximal, characteristic, complemented
2C22×#6505C211yesmaximal, characteristic
3C2×#90213C211yesmaximal, characteristic
4C2×C7×#419C211yesmaximal, characteristic, complemented
5C2×#89905C211yesmaximal, characteristic
6C2×M16×Dic7C211yesmaximal, characteristic, complemented
7C2×#89767C211yesmaximal, characteristic, complemented
8#11736391C2116yesmaximal, direct product factor
9C2×#89561C212yesmaximal, complemented
10C2×#89589C212yesmaximal, complemented
11C2×#89562C212yesmaximal, complemented
12C2×#89560C212yesmaximal, complemented
13C23×C7×Q8C2211yescharacteristic
14C22×#1157C2211yescharacteristic
15C22×C7×M16C2211yescharacteristic
16C2×C7×#117C2211yescharacteristic
17C2×Q8×Dic7—21no—
18C2×Q8×Dic7—21no—
19C2×Q8×Dic7—24no—
20C2×Q8×Dic7C2212yes—
21C2×Q8×Dic7C2212yes—
22C2×Q8×Dic7C2218yescomplemented
23C22×#1144C2212yes—
24C2×#6505C4116yescomplemented
25C2×#6505C2218yes—
26C22×#1143C2212yes—
27C22×C4⋊Dic7—21no—
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4×Dic7—21no—
30C22×C4×Dic7C2211yescharacteristic
31C22×#1136C2211yescharacteristic
32#90213—24no—
33#90213C2218yes—
34C2×#6456C2211yescharacteristic
35C2×#6456C2211yescharacteristic
36C2×#6450C2211yescharacteristic
37C2×#6450C2211yescharacteristic
38C2×(C22⋊D7)⋊C4—21no—
39C2×(C22⋊D7)⋊C4—21no—
40C2×#6435—21no—
41C2×C42×D7—21no—
42C7×#419C2218yescomplemented
43C2×C7×#103C2212yes—
44C2×C7×#103C2212yes—
45#89905C2218yes—
46M16×Dic7C2218yescomplemented
47C2×#6395C2212yes—
48C2×#6390C2212yes—
49C2×#6389C2212yes—
50C2×C8×Dic7C2212yes—
51#89767C2218yescomplemented
52C2×#6382C2212yes—
53C2×#6381C2212yes—
54#89589C22116yescomplemented
55#89562C22116yescomplemented
56#89561C22116yescomplemented
57#89560C22116yescomplemented
58C2×C4×#137—71nomaximal, Sylow
59C22×C7×Q8—21no—
60C22×C7×Q8—22no—
61C22×C7×Q8—24no—
62C22×C7×Q8C2×C418yescomplemented
63C22×C7×Q8C2312yes—
64C22×C7×Q8C2314yes—
65C23×C4×C7—21no—
66C23×C4×C7C2311yescharacteristic
67C22×C22⋊D7—21no—
68C23×Dic7—21no—
69C23×Dic7D411yescharacteristic
70C23×Dic7D411yescharacteristic
71C2×#1157—22no—
72C2×#1157—24no—
73C2×#1157C2×C418yes—
74C2×#1157C2314yes—
75C22×D28C2311yescharacteristic
76C22×C4×D7—21no—
77C22×C4×D7—21no—
78C22×C4×D7—21no—
79C22×Dic14C2311yescharacteristic
80C2×C7×M16—24no—
81C2×C7×M16C2314yes—
82C22×C7×C8C2312yes—
83C7×#117—22no—
84C7×#117C2314yes—
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C4⋊C4C2311yescharacteristic
87C2×C7×C22⋊C4—21no—
88C2×C42×C7—21no—
89Q8×Dic7—24no—
90Q8×Dic7—24no—
91Q8×Dic7—28no—
92Q8×Dic7—28no—
93Q8×Dic7C2318yes—
94Q8×Dic7C2318yes—
95C2×#1144C2×C4116yescomplemented
96C2×#1144C2318yes—
97#6505C2×C4164yescomplemented
98C2×#1143C2×C4116yescomplemented
99C2×#1143C2318yes—
100C2×(C2×D7)⋊C4—21no—
101C2×(C2×D7)⋊C4—21no—
102C2×C4⋊Dic7—21no—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—28no—
107C2×C4⋊Dic7C2312yes—
108C2×C4⋊Dic7C2314yes—
109C2×Dic7⋊C4—21no—
110C2×Dic7⋊C4—21no—
111C2×C4×Dic7—21no—
112C2×C4×Dic7—21no—
113C2×C4×Dic7—22no—
114C2×C4×Dic7—22no—
115C2×C4×Dic7—28no—
116C2×C4×Dic7D411yescharacteristic
117C2×C4×Dic7D411yescharacteristic
118C2×C4×Dic7D414yes—
119C2×C4×Dic7C2311yescharacteristic
120C2×C4×Dic7C2311yescharacteristic
121C2×C4×Dic7C2314yes—
122C2×#1136C2×C418yescomplemented
123C2×#1136C2314yes—
124C22×C7⋊C8C2312yes—
125#6456—22no—
126#6456—22no—
127#6456C2314yes—
128#6456C2314yes—
129#6450—22no—
130#6450—22no—
131#6450C2314yes—
132#6450C2314yes—
133(C22⋊D7)⋊C4—28no—
134(C22⋊D7)⋊C4—28no—
135#6435—28no—
136C42×D7—28no—
137C7×#103C2318yes—
138C7×#103C2318yes—
139#6395C2318yes—
140#6390C2318yes—
141#6389C2318yes—
142C8×Dic7C2318yes—
143#6382C2318yes—
144#6381C2318yes—
145C22×#137—71no—
146C2×C4×#41—71no—
147C22×C4×Q8—71no—
148C4×#137—716no—
149C2×#441—72no—
150C2×#440—72no—
151C2×C4×Q16—72no—
152C2×C4×SD16—72no—
153C2×#428—71no—
154C2×#417—71no—
155C2×#419D711yescharacteristic, complemented
156C2×C4×M16—71no—
157C24×C7C2×D411yescharacteristic
158C23×D7—21no—
159C2×C7×Q8—28no—
160C2×C7×Q8—216no—
161C2×C7×Q8—24no—
162C2×C7×Q8—22no—
163C2×C7×Q8—24no—
164C2×C7×Q8—28no—
165C2×C7×Q8C22×C418yes—
166C2×C7×Q8C22×C4116yescomplemented
167C2×C7×Q8C2414yes—
168C22×C4×C7—28no—
169C22×C4×C7—22no—
170C22×C4×C7—24no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7C22×C414yes—
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D412yes—
176C22×C4×C7#4114yes—
177C22×C4×C7C2411yescharacteristic
178C22×C4×C7C2412yes—
179C2×C22⋊D7—28no—
180C2×C22⋊D7—24no—
181C22×Dic7—21no—
182C22×Dic7—24no—
183C22×Dic7—24no—
184C22×Dic7—22no—
185C22×Dic7—42no—
186C22×Dic7—44no—
187C22×Dic7C2×D414yes—
188C22×Dic7C2×D411yescharacteristic
189C22×Dic7C2×D411yescharacteristic
190C22×Dic7C2×D411yescharacteristic
191C22×Dic7C2×D414yes—
192C22×Dic7C2×D411yescharacteristic
193#1157—216no—
194#1157—28no—
195#1157C22×C4116yes—
196C2×D28—21no—
197C2×D28—22no—
198C2×D28C22×C414yes—
199C2×D28C2412yes—
200C2×C4×D7—28no—
201C2×C4×D7—24no—
202C2×C4×D7—24no—
203C2×C4×D7—24no—
204C2×C4×D7—44no—
205C2×C4×D7—44no—
206C2×Dic14—21no—
207C2×Dic14—22no—
208C2×Dic14C22×C414yes—
209C2×Dic14C2412yes—
210C7×M16—28no—
211C2×C7×C8—24no—
212C2×C7×C8C2414yes—
213C7×C4⋊C4—21no—
214C7×C4⋊C4—21no—
215C7×C4⋊C4C2412yes—
216C7×C4⋊C4C2412yes—
217C7×C22⋊C4—24no—
218C42×C7—24no—
219#1144C22×C4132yescomplemented
220#1143C22×C4132yescomplemented
221(C2×D7)⋊C4—24no—
222(C2×D7)⋊C4—24no—
223C4⋊Dic7—24no—
224C4⋊Dic7—22no—
225C4⋊Dic7—28no—
226C4⋊Dic7—28no—
227C4⋊Dic7C2414yes—
228Dic7⋊C4—24no—
229Dic7⋊C4—24no—
230C4×Dic7—24no—
231C4×Dic7—24no—
232C4×Dic7—28no—
233C4×Dic7—28no—
234C4×Dic7C2×D414yes—
235C4×Dic7C2×D414yes—
236C4×Dic7C2×D412yes—
237C4×Dic7C2×D412yes—
238C4×Dic7C2412yes—
239C4×Dic7C2412yes—
240#1136C22×C4116yescomplemented
241C2×C7⋊C8C22×C418yes—
242C2×C7⋊C8C2414yes—
243C22×#41—71no—
244C23×Q8C2×D711yescharacteristic
245C2×#137—716no—
246C2×#137—78no—
247C22×Q16—72no—
248C22×SD16—72no—
249C22×M16—71no—
250C22×M16C2×D711yescharacteristic
251C4×#41—78no—
252C4×#41—144no—
253C2×C4×Q8—72no—
254C2×C4×Q8—72no—
255C2×C4×Q8—78no—
256C2×C4×Q8—71no—
257C2×C4×Q8—71no—
258C2×C4×Q8—141no—
259C2×C4×Q8—144no—
260C2×C4×Q8—141no—
261C2×C4×D4—71no—
262C2×C4×D4—71no—
263C2×C4×D4—141no—
264C2×C4×D4—141no—
265C2×#117—141no—
266C2×#117C2×D711yescharacteristic
267C22×C4⋊C4—71no—
268C22×C4⋊C4—141no—
269C22×C42—71no—
270C22×C42—141no—
271C22×C42—141no—
272#441—716no—
273#440—716no—
274C4×Q16—716no—
275C4×SD16—716no—
276#428—78no—
277C2×#107—72no—
278C2×#106—72no—
279#419C2×D718yescomplemented
280#417—78no—
281C2×#103—72no—
282C2×#103C2×D712yes—
283C2×#103C2×D712yes—
284C2×#102—72no—
285C4×M16—78no—
286C2×#97—72no—
287C2×C4×C8—72no—
288C23×C7—22no—
289C23×C7—22no—
290C23×C7C4×D414yes—
291C23×C7C22×D412yes—
292C23×C7C22×D411yescharacteristic
293C22×D7—24no—
294C22×D7—22no—
295C22×D7—42no—
296C22×D7—42no—
297C7×Q8—28no—
298C7×Q8—216no—
299C7×Q8—24no—
300C7×Q8C23×C418yes—
301C2×C4×C7—28no—
302C2×C4×C7—216no—
303C2×C4×C7—24no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—42no—
307C2×C4×C7—42no—
308C2×C4×C7C4×D414yes—
309C2×C4×C7C4×D418yes—
310C2×C4×C7C23×C412yes—
311C2×C4×C7C23×C414yes—
312C2×C4×C7C22×D412yes—
313C2×C4×C7C22×D411yescharacteristic
314C2×C4×C7C2×#4112yes—
315C2×C4×C7C2×#4114yes—
316C2×C4×C7C2511yescharacteristic
317C22⋊D7—216no—
318C2×Dic7—24no—
319C2×Dic7—22no—
320C2×Dic7—22no—
321C2×Dic7—22no—
322C2×Dic7—22no—
323C2×Dic7—28no—
324C2×Dic7—24no—
325C2×Dic7—44no—
326C2×Dic7—48no—
327C2×Dic7—44no—
328C2×Dic7#13714yescomplemented
329C2×Dic7C22×D412yes—
330C2×Dic7C22×D412yes—
331C2×Dic7C22×D412yes—
332C2×Dic7C22×D412yes—
333D28—24no—
334D28—22no—
335D28C23×C414yes—
336C4×D7—216no—
337C4×D7—48no—
338C4×D7—48no—
339Dic14—24no—
340Dic14—22no—
341Dic14C23×C414yes—
342C7×C8—24no—
343C7⋊C8C23×C418yes—
344C2×#41—78no—
345C2×#41—74no—
346C2×#41—142no—
347C2×#41—144no—
348C22×Q8—22no—
349C22×Q8—21no—
350C22×Q8—24no—
351C22×Q8—71no—
352C22×Q8C4×D718yescomplemented
353C22×Q8C22×D712yes—
354C22×Q8C22×D714yes—
355C22×D4—71no—
356C22×D4—141no—
357C23×C4—21no—
358C23×C4—71no—
359C23×C4—71no—
360C23×C4—141no—
361C23×C4—141no—
362C23×C4—141no—
363C23×C4—141no—
364C23×C4C22×D711yescharacteristic
365#137—764no—
366C2×Q16—716no—
367C2×Q16—78no—
368C2×SD16—716no—
369C2×SD16—78no—
370C2×M16—24no—
371C2×M16—78no—
372C2×M16—74no—
373C2×M16C22×D714yes—
374C22×C8—72no—
375C22×C8C22×D712yes—
376C4×Q8—78no—
377C4×Q8—78no—
378C4×Q8—74no—
379C4×Q8—74no—
380C4×Q8—142no—
381C4×Q8—142no—
382C4×Q8—148no—
383C4×Q8—148no—
384C4×Q8—144no—
385C4×Q8—144no—
386C4×D4—74no—
387C4×D4—74no—
388C4×D4—142no—
389C4×D4—142no—
390C4×D4—148no—
391C4×D4—148no—
392#117—22no—
393#117—148no—
394#117C22×D714yes—
395C2×C4⋊C4—72no—
396C2×C4⋊C4—74no—
397C2×C4⋊C4—148no—
398C2×C4⋊C4—142no—
399C2×C4⋊C4—142no—
400C2×C4⋊C4—141no—
401C2×C4⋊C4—141no—
402C2×C4⋊C4—142no—
403C2×C4⋊C4—141no—
404C2×C4⋊C4C22×D711yescharacteristic
405C2×C4⋊C4C22×D711yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—141no—
408C2×C22⋊C4—141no—
409C2×C42—21no—
410C2×C42—71no—
411C2×C42—74no—
412C2×C42—71no—
413C2×C42—71no—
414C2×C42—71no—
415C2×C42—74no—
416C2×C42—148no—
417C2×C42—141no—
418C2×C42—141no—
419C2×C42—148no—
420C2×C42—142no—
421C2×C42—142no—
422#107—78no—
423#106—78no—
424#103—78no—
425#103C22×D718yes—
426#103C22×D718yes—
427#102—78no—
428#97—78no—
429C4×C8—78no—
430C22×C7—28no—
431C22×C7—22no—
432C22×C7—22no—
433C22×C7C2×C4×D414yes—
434C22×C7C2×C4×D412yes—
435C22×C7C2×#13712yes—
436C22×C7#57512yes—
437C22×C7C23×D411yescharacteristic
438C2×D7—24no—
439C2×D7—48no—
440C2×D7—42no—
441C2×D7—42no—
442C4×C7—28no—
443C4×C7—42no—
444C4×C7—42no—
445C4×C7C2×C4×D412yes—
446C4×C7C2×C4×D414yes—
447C4×C7C24×C411yescharacteristic
448C4×C7C22×#4111yescharacteristic
449Dic7—24no—
450Dic7—22no—
451Dic7—22no—
452Dic7—22no—
453Dic7—44no—
454Dic7C2×#13714yescomplemented
455C24—141no—
456C24D4×D711yescharacteristic
457#41—716no—
458#41—1416no—
459#41—148no—
460C2×Q8—28no—
461C2×Q8—216no—
462C2×Q8—24no—
463C2×Q8—22no—
464C2×Q8—24no—
465C2×Q8—28no—
466C2×Q8—74no—
467C2×Q8—72no—
468C2×Q8—141no—
469C2×Q8—142no—
470C2×Q8C2×C4×D718yes—
471C2×Q8C2×C4×D7116yescomplemented
472C2×Q8C23×D714yes—
473C2×D4—74no—
474C2×D4—72no—
475C2×D4—148no—
476C2×D4—144no—
477C2×D4—141no—
478C2×D4—142no—
479C22×C4—28no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—71no—
485C22×C4—74no—
486C22×C4—71no—
487C22×C4—71no—
488C22×C4—71no—
489C22×C4—74no—
490C22×C4—144no—
491C22×C4—144no—
492C22×C4—144no—
493C22×C4—141no—
494C22×C4—148no—
495C22×C4—144no—
496C22×C4—144no—
497C22×C4—142no—
498C22×C4—284no—
499C22×C4—284no—
500C22×C4—282no—
501C22×C4—284no—
502C22×C4C2×C4×D714yes—
503C22×C4D4×D712yes—
504C22×C4D4×D711yescharacteristic
505C22×C4#115914yes—
506C22×C4C23×D712yes—
507C22×C4C23×D711yescharacteristic
508Q16—732no—
509SD16—732no—
510M16—28no—
511M16—716no—
512C2×C8—24no—
513C2×C8—78no—
514C2×C8—74no—
515C2×C8C23×D714yes—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—74no—
519C4⋊C4—144no—
520C4⋊C4—144no—
521C4⋊C4—148no—
522C4⋊C4—148no—
523C4⋊C4—144no—
524C4⋊C4—142no—
525C4⋊C4C23×D712yes—
526C4⋊C4C23×D712yes—
527C22⋊C4—24no—
528C22⋊C4—144no—
529C22⋊C4—144no—
530C42—24no—
531C42—74no—
532C42—74no—
533C42—72no—
534C42—72no—
535C42—72no—
536C42—72no—
537C42—144no—
538C42—144no—
539C42—148no—
540C42—148no—
541C2×C7—24no—
542C2×C7C4×#13714yescomplemented
543C2×C7C22×C4×D411yescharacteristic
544C2×C7C22×#13711yescharacteristic
545C2×C7C2×#57511yescharacteristic
546D7—44no—
547C23—22no—
548C23—22no—
549C23—144no—
550C23—142no—
551C23—282no—
552C23—282no—
553C23(C22⋊D7)⋊C414yes—
554C23C2×D4×D712yes—
555C23C2×D4×D711yescharacteristic
556Q8—28no—
557Q8—216no—
558Q8—24no—
559Q8—74no—
560Q8—144no—
561Q8—142no—
562Q8C22×C4×D718yes—
563D4—74no—
564D4—1416no—
565D4—144no—
566D4—142no—
567C2×C4—28no—
568C2×C4—216no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—74no—
575C2×C4—72no—
576C2×C4—72no—
577C2×C4—72no—
578C2×C4—72no—
579C2×C4—148no—
580C2×C4—144no—
581C2×C4—142no—
582C2×C4—142no—
583C2×C4—142no—
584C2×C4—142no—
585C2×C4—1416no—
586C2×C4—144no—
587C2×C4—288no—
588C2×C4—288no—
589C2×C4—284no—
590C2×C4—288no—
591C2×C4—284no—
592C2×C4(C22⋊D7)⋊C414yes—
593C2×C4(C22⋊D7)⋊C418yes—
594C2×C4C22×C4×D712yes—
595C2×C4C22×C4×D714yes—
596C2×C4C2×D4×D712yes—
597C2×C4C2×D4×D711yescharacteristic
598C2×C4C2×#115912yes—
599C2×C4C2×#115914yes—
600C2×C4C24×D711yescharacteristic
601C8—24no—
602C8—78no—
603C7C2×C4×#13711yescharacteristic, complemented, Sylow
604C22—22no—
605C22—22no—
606C22—28no—
607C22—144no—
608C22—282no—
609C22—282no—
610C22—288no—
611C22C2×(C22⋊D7)⋊C414yes—
612C22C2×(C22⋊D7)⋊C412yes—
613C22D7×#13712yes—
614C22#9046812yes—
615C22C22×D4×D711yescharacteristic
616C4—28no—
617C4—42no—
618C4—42no—
619C4—74no—
620C4—142no—
621C4—142no—
622C4—142no—
623C4—144no—
624C4—284no—
625C4C2×(C22⋊D7)⋊C414yes—
626C4C2×(C22⋊D7)⋊C412yes—
627C4C23×C4×D711yescharacteristic
628C4C22×#115911yescharacteristic
629C2—24no—
630C2—284no—
631C2#1173639114yesdirect product factor
632C2C22×(C22⋊D7)⋊C411yescharacteristic
633C2C2×D7×#13711yescharacteristic
634C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#419C2
socleC23×C7C22×D4
prime radicalC22×#1157C22
cosocleC2×C4×C7C25
hypercenterC2×#419D7
hypocenterC7C2×C4×#137
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×Q8×Dic7C2semidirect
4. C2×C7×#419C2semidirect
6. C2×M16×Dic7C2semidirect
7. C2×#89767C2semidirect
8. #11736391C2direct (N × H)
9. C2×#89561C2semidirect
10. C2×#89589C2semidirect
11. C2×#89562C2semidirect
12. C2×#89560C2semidirect
22. C2×Q8×Dic7C22semidirect
24. C2×#6505C4semidirect
42. C7×#419C22semidirect
46. M16×Dic7C22semidirect
51. #89767C22semidirect
54. #89589C22semidirect
55. #89562C22semidirect
56. #89561C22semidirect
57. #89560C22semidirect
62. C22×C7×Q8C2×C4semidirect
95. C2×#1144C2×C4semidirect
97. #6505C2×C4semidirect
98. C2×#1143C2×C4semidirect
122. C2×#1136C2×C4semidirect
155. C2×#419D7semidirect
166. C2×C7×Q8C22×C4semidirect
219. #1144C22×C4semidirect
220. #1143C22×C4semidirect
240. #1136C22×C4semidirect
279. #419C2×D7semidirect
328. C2×Dic7#137semidirect
352. C22×Q8C4×D7semidirect
454. Dic7C2×#137semidirect
471. C2×Q8C2×C4×D7semidirect
542. C2×C7C4×#137semidirect
603. C7C2×C4×#137semidirect
631. C2#11736391direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×Q8×Dic72
C22×#65052
C2×#902132
C2×C7×#4192
C2×#899052
C2×M16×Dic72
C2×#897672
#117363912
C2×#895612
C2×#895892
C2×#895622
C2×#895602
C2×C4×#1377